The Antimatter Calculator

Ensign Garrovick: "Just think, Captain. Less than one ounce of antimatter here, it's more powerful than ten thousand cobalt bombs."

Captain Kirk: "Let's hope it's as powerful as man will ever get."

The truth about the destructive potential of antimatter is considerably less dramatic. One ounce of antimatter equates to 1.22 megatons, which is comparable to a single modern day H-bomb. In order to help prevent such mistakes from occurring in the future, I present the anti-matter caculator. Just plug in the amount of antimatter you're thinking of using and the calculator will return just how much destructive force it contains.

Step 1. Indicate the unit of measure Pounds Ounces Kilograms Tons
Step 2. Enter the amount of antimatter here:
Step 3. Hit the compute button
Step 4. Behold the results below:
 

A megaton is a unit of energy approximately equivalent to the energy released
in the detonation of 1,000,000 tons of TNT. Used to specify the energy output, and hence
destructive power, of nuclear weapons.

A kiloton is one-thousandth of a megaton.

To put things in perspective, here are some famous explosions from history and theory
along with their yields:

EventYield
Seymour Narrows, British Columbia 1958. 1,375 tons of chemical explosives.1.375 kilotons
Little Boy, the atomic bomb dropped on Hiroshima, Japan on August 6, 1945.13 kilotons.
Fat man, the atomic bomb dropped on Nagasaki, Japan on August 9, 1945.20 kilotons.
One ounce of antimatter1.22 megatons
Starfish Prime, July 9, 1962. Detonation of a Hydrogen bomb at 16 degrees, 28 minutes North latitude, 169 degrees, 38 minutes West longitude, 250 miles altitude.1.45 megatons
The Tanguska / Tunguska Event (spelling is in dispute), suspected comet impact in Tanguska, Russia on June 30, 1908.10 megatons
The Bravo test, one of the Bikini Atoll bomb tests. February 1954, was, at 15 megatons, the most powerful bomb ever detonated by the United States--far bigger than expected.15 megatons
One pound of antimatter19.5 megatons
Mount St. Helens May 18, 1980.24 megatons
The 2004 Indian Ocean earthquake. December 26, 2004 at 00:58:53 UTC. An undersea earthquake with an epicentre off the west coast of Sumatra, Indonesia. The earthquake generated a tsunami that is considered one of the deadliest natural disasters in history.26.3 megatons
Tsar Bomba, the largest nuclear weapon ever detonated 11:32 AM 30 October 1961 (Moscow Time) Such a device could be souped up to deliver a 100 megaton blast.50 megatons
The third 1883 eruption of Krakatoa150 megatons
Hurricane Katrina hitting the Gulf Coast. At full power, a hurricane like Katrina releases 10 megatons every 20 minutes.300 megatons
World War III, computed as the simultaneous explosion of all known nuclear devices (about 15,000 today).10,000 megatons
"Dinosaur Killer" Impact of 10-15 km asteroid traveling at 20 kilometers per second.100,000,000 megatons or 10^8 megatons
The destruction of Alderan, which I computed as the amount of energy required to give an Earth-sized planet its own escape velocity. 819,083,688.72 megatons
A supernova, an explosion powerful enough to destroy a solar system.one billion billion billion megatons or 10^27 megatons

The Math

Several people have asked to see the math behind the calculations above.

We start with Einstein's famous equation E = M*C^2

(The energy contained within a given amount of mass = That mass times the speed of light squared)

E is expressed in joules, which is kilograms times (meters/second)^2, so the first thing is to convert 1 pound into it's equivalent in kg.

(A few people who wrote me on this had problems because they used grams instead of kilograms. If your answer is 1,000 times greater than mine, that's your problem)

1 ounce equates to 0.02835 kilograms (rounding to 5 decimal places).

Aside:
Be careful here. Pounds are a measure of weight and kilograms are a measure of mass. An objects weight can vary while its mass remains constant. I presume here that we're talking one pound of mass at sea level on earth halfway between the equator and one of the poles. I never saw Captain Kirk on a planet that didn't have 9.8 m/s^2 for some reason.

Aside
English to metric conversion was the real killer on this project.

Also, we have to annihilate the antimatter with an equal amount of matter, so 2 * 0.02835 = 0.05670 kg.

Aside:
Anti-matter annihilation expresses its energy as a burst of high-frequency gamma radiation and high-speed neutrinos. Drop a pound of antimatter on the floor and you'll see a bright flash of light and then nothing else for the remainder of your very short life! The difficulty in getting antimatter to "blow up" is one reason why the US never developed an antimatter bomb.

(0.05670 kg) * (2.9979e8 m/s ^ 2) = 5.09577E+15 joules

There are 4.18e15 joules in a megaton, so 5.09577E+15 joules dvided by 4.18e15 equates to 1.21908 megatons.

How Did Antimatter Get To Be So Over-rated?

I blame television in general and Star Trek in particular.

While developing the pilot for this new series, Gene Roddenberry asked a number of scientists for feedback on his pilot script The Cage. One of the points brought up was the power source for the ship. Here's the relevant quote on the subject from The Making of Star Trek by Stephen E. Whitfield and Gene Roddenberry:

Discussions with scientific consultants had already ruled out atomic power as inefficient and inadequate for achieving hyper-light speeds. Ion drive was ruled out for the same reason.

Finally, the conclusion reached was that the only power source conceivably large enough to do the job would be the energy released by the sheer annihilation of matter and anti-matter. This had already been achieved on a minute scale by several research laboratories. Theoretical release of such power, on Star Trek's scale, compares to nuclear energy as an H-bomb compares to a kitchen match!

Now the statement compares to nuclear energy as an H-bomb compares to a kitchen match! is very dramatic and impressive-sounding, but not terribly helpful for calculating exact yields. Most of the writers who wrote for Star Trek were not scientists or even science-fiction writers, which meant the above statement was all that they had to work with.

References

Star Trek (Original Series, season 2) Obsession Writer: Art Wallace. Directed by Ralph Senensky Stardate 3619.2, airdate 12/15/1967

Star Trek Concordance Copyright (C) 1976 by Paramount Pictures Corporation and Bjo Trimble ISBN 0-345-25137-695

The Making of Star Trek Copyright (C) 1968 by Stephen E. Whitfield SBN 345-24691-8-195